Efficient multipole representation for matter-wave optics

TL;DR

This paper introduces a three-dimensional multipole expansion method for describing complex matter-wave fields and optical devices, enabling improved analysis and optimization of matter-wave optics systems.

Contribution

It presents a novel 3D multipole expansion framework for matter-wave optics, extending beam optics techniques to complex 3D matter-wave fields and traps.

Findings

Characterizes real magnetic and optical traps using spherical harmonics and polynomials.

Analyzes aberrations in expanding Bose-Einstein condensates in 3+1 dimensions.

Identifies deviations from quadratic phase in scaling approximations.

Abstract

Technical optics with matter waves requires a universal description of three-dimensional traps, lenses, and complex matter-wave fields. In analogy to the two-dimensional Zernike expansion in beam optics, we present a three-dimensional multipole expansion for Bose-condensed matter waves and optical devices. We characterize real magnetic chip traps, optical dipole traps, and the complex matter-wave field in terms of spherical harmonics and radial Stringari polynomials. We illustrate this procedure for typical harmonic model potentials as well as real magnetic and optical dipole traps. Eventually, we use the multipole expansion to characterize the aberrations of a ballistically interacting expanding Bose-Einstein condensate in (3+1)-dimensions. In particular, we find deviations from the quadratic phase ansatz in the popular scaling approximation. This universal multipole description of aberrations can be used to optimize matter-wave optics setups, for example in matter-wave interferometers.